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Mathematical Statistics - Second Edition
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This Book is the second edition that intended to be textbook studied for undergraduate/ postgraduate course in mathematical statistics. In order to achieve the goals of the book, it is divided into the following chapters. Chapter One introduces events and probability review. Chapter Two devotes to random variables in their two types: discrete and continuous with definitions of probability mass function, probability density function and cumulative distribution function as well. Chapter Three discusses mathematical expectation with its special types such as: moments, moment generating function and other related topics. Chapter Four deals with some special discrete distributions: (Discrete Uniform, Bernoulli, Binomial, Poisson, Geometric, Negative Binomial and Hypergeometric) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Chapter Five deals with some special continuous distributions: (Uniform, Normal, Exponential, Gamma and Beta) with their mathematical formulas of p.m.f., C.D.F. and m.g.f. Many solved examples are intended in this book (obtaining mean and variance of distributions by m.g.f.). Chapter Six introduces univariate discrete and continuous transformations, i.e., one dimensional variables and their yielding probability distributions. Chapter Seven devotes to truncation of distributions from left, right or both sides, beside the probability distribution of order statistics. Chapter Eight discusses mathematical features of joint, marginal and conditional distributions, as well as independency via covariance and correlation of bivariate distributions. Chapter Nine deals with some special topics such as getting distribution for some transformation from multidimensional random variables by using moment generating function (m.g.f.) and cumulative distribution function (C.D.F.) Many solved examples (about 100) are intended in this book, in addition to a variety of unsolved relied problems (about 150) at the end of each chapter to enrich the statistical knowledge of our readers.

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Publication Date
Fri Jan 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Quasi Semi and Pseudo Semi (p,E)-Convexity in Non-Linear Optimization Programming
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The class of quasi semi -convex functions and pseudo semi -convex functions are presented in this paper by combining the class of -convex functions with the class of quasi semi -convex functions and pseudo semi -convex functions, respectively. Various non-trivial examples are introduced to illustrate the new functions and show their relationships with -convex functions recently introduced in the literature. Different general properties and characteristics of this class of functions are established. In addition, some optimality properties of generalized non-linear optimization problems are discussed. In this generalized optimization problems, we used, as the objective function, quasi semi -convex (respectively, strictly quasi semi -convex

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Publication Date
Sat Sep 30 2023
Journal Name
Iraqi Journal Of Science
Reliability Estimation for the Exponential-Pareto Hybrid System
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     The reliability of hybrid systems is important in modern technology, specifically in engineering and industrial fields; it is an indicator of the machine's efficiency and ability to operate without interruption for an extended period of time. It also allows for the evaluation of machines and equipment for planning and future development. This study looked at reliability of hybrid (parallel series) systems with asymmetric components using exponential and Pareto distributions. Several simulation experiments were performed to estimate the reliability function of these systems using the Maximum Likelihood method  and the Standard Bayes method  with a quadratic loss (QL) function and two priors: non-informative (Jeffery) and inform

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Publication Date
Tue Feb 13 2024
Journal Name
Iraqi Journal Of Science
Parameters Estimation for Modified Weibull Distribution Based on Type One Censored Samplest
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The three parameters distribution called modified weibull distribution (MWD) was introduced first by Sarhan and Zaindin (2009)[1]. In theis paper, we deal with interval estimation to estimate the parameters of modified weibull distribution based on singly type one censored data, using Maximum likelihood method and fisher information to obtain the estimates of the parameters for modified weibull distribution, after that applying this technique to asset of real data which taken for Leukemia disease in the hospital of central child teaching .

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Publication Date
Thu Sep 15 2022
Journal Name
Al-academy
Interaction and functional structural transformation of product design
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The research discussed the propositions of functional structures and the requirements for their transformation according to the variables of use and human interaction through the variables of functions with one form products، multifunctional variables، and transforming form in one product. The patterns of user’s interaction with products were discussed through the variables of functional type، starting from defining the types of functions in the industrial product structures to: practical functions، which were classified into: informational functions، ergonomic functions، use، handling، comfort، global، anthropometric adaptation and physical postures. While the interaction variables were discussed according to the meaning fun

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Publication Date
Thu Dec 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
Measuring and Analysis of Demand Function on Oil derivatives of A Selected countries the Period 1985- 2008
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The subject of demand on oil derivative has occupied an important position at present time in the daily life context. The fuel of benzene and gas oil and kerosene is one of basic elements of that concern, and on local , regional and international levels. The oil derivatives have played a leading role in determining the course and nature of development since early 1970 to the present time whether in the productive Arab countries or the importing. The researcher set out from the hypothesis that the increase of the local consumer demand on some of the oil derivatives is because of the internal and external factors accompanied by the inability of the productive capability and local production to confront this increase, and the resort

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Publication Date
Fri Sep 15 2023
Journal Name
Al-academy
Space suitability and its functional implications in interior design
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The current research dealt with the study of space compatibility and its role in enhancing the functional aspect of the design of the interior spaces of isolation hospitals by finding a system or format that is compatible with the nature of the changes occurring in the structure and function of the space system, as well as contributing to enhancing compatibility between the functional aspect and the interior space. Therefore, the designer must The interior is the study of the functional and spatial aspects as they are the basic aspects for achieving suitability, and through the interaction between the person and the place, the utilitarian performance characteristics are generated that the interior designer is interested in and tries to d

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Publication Date
Sun Apr 30 2023
Journal Name
Iraqi Journal Of Science
Effect of High Dose of Soybean Meal on the Histology and Function of the Thyroid Gland in Albino Rat at Pre- and Postpuberty
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The study aimed to determine the effect of soybean meal on the histological
structure and some functional parameters of the thyroid gland was investigated in
this study. For this purpose, 24 white male rats were divided into four groups each
of six rats, as following (G1): normal control rats, at the prepubertal life stage, were
dissected after 40 days from the weaning (i.e., from Postnatal Day "PND" 21),
(G2): prepubertal rats, were treated with high dose of soybean meal "40% of daily
diet" for 40 days after the weaning, (G3): normal control rats, at the postpubertal
stage, were dissected after 40 days from the puberty (i.e., from PND 60), (G4):
postpubertal rats, were treated with high dose of soybean meal (40%)

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Publication Date
Sun Dec 01 2019
Journal Name
Gene Reports
Hepatitis B virus genotypes among chronic hepatitis B patients from Baghdad, Iraq and their impact on liver function
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Hepatitis B virus (HBV) infection is a significant global health problem. Populations of different ethnicities show great heterogeneity in HBV genotype frequency distributions. A cross-sectional study was conducted during June–October 2018 to determine frequency of HBV genotypes among chronic HBV patients from Baghdad, Iraq. The method of detection was nested polymerase chain reaction system. Further, the study assessed the impact of HBV genotypes on serum level of liver-function tests: total serum bilirubin, alkaline phosphatase, alanine aminotransferase and aspartate aminotransferase. Eighty chronic HBV patients were enrolled in the study. Six HBV genotypes were identified (A, B, C, D, E and F). The most frequently encountered genotypes

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Publication Date
Mon May 28 2018
Journal Name
Iraqi Journal Of Science
Study the protective effect of Matricaria chamomilla flower extract against the toxicity of Entamoeba histolytica induces liver and renal dysfunctions in adult albino male rats
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The present study was designed to show the potential role of Matricaria chamomilla flower extract against toxicity of Entamoeba histolytica  . The study used 20 adult albino male rats that divide randomly to four groups (each group consist 5 rats); control group received ad libidium, group of rats administrated with 1X103 cyct/ml suspension for seven days, group of rats administrated with 1X103 cyct/ml suspension and treated with 50mg/kg extract for month, group of rats administrated with 1X103 cyct/ml suspension and treated with 100mg/kg extract for month. The results show high significant increased (P < 0.05) in levels of Alanine

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Publication Date
Tue Dec 01 2020
Journal Name
Journal Of Engineering
Performance of 2- Link Robot by utilizing Adaptive Sliding Mode Controller
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The Sliding Mode Control (SMC) has been among powerful control techniques increasingly. Much attention is paid to both theoretical and practical aspects of disciplines due to their distinctive characteristics such as insensitivity to bounded matched uncertainties, reduction of the order of sliding equations of motion, decoupling mechanical systems design. In the current study, two-link robot performance in the Classical SMC is enhanced via Adaptive Sliding Mode Controller (ASMC) despite uncertainty, external disturbance, and coulomb friction. The key idea is abstracted as follows: switching gains are depressed to the low allowable values, resulting in decreased chattering motion and control's efforts of the two-link robo

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